lmomTLgpa {lmomco} | R Documentation

## Trimmed L-moments of the Generalized Pareto Distribution

### Description

This function estimates the symmetrical trimmed L-moments (TL-moments) for t=1 of the Generalized Pareto distribution given the parameters (xi, α, and kappa) from `parTLgpa`. The TL-moments in terms of the parameters are

λ^{(1)}_1 = xi + frac{α(kappa+5)}{(kappa+3)(kappa+2)} mbox{,}

λ^{(1)}_2 = frac{6α}{(kappa+4)(kappa+3)(kappa+2)} mbox{,}

tau^{(1)}_3 = frac{10(1-kappa)}{9(kappa+5)} mbox{, and}

tau^{(1)}_4 = frac{5(kappa-1)(kappa-2)}{4(kappa+6)(kappa+5)} mbox{.}

### Usage

    lmomTLgpa(para)

### Arguments

`para` | The parameters of the distribution.

### Value

An R `list` is returned.

`lambdas` | Vector of the TL-moments. First element is λ^{(1)}_1, second element is λ^{(1)}_2, and so on.
`ratios` | Vector of the L-moment ratios. Second element is tau^{(1)}, third element is tau^{(1)}_3 and so on.
`trim` | Trim level = 1
`source` | An attribute identifying the computational source of the TL-moments: “lmomTLgpa”.

### Author(s)

W.H. Asquith

### References

Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational Statistics and Data Analysis, vol. 43, pp. 299–314.

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

### See Also

`parTLgpa`, `quagpa`, `cdfgpa`

### Examples

    TL <- TLmoms(c(123,34,4,654,37,78,21,3400),trim=1)
    TL
    lmomTLgpa(parTLgpa(TL))

[Package lmomco version 0.92 Index]